Manipulators, robots, haptic devices or more generally devices for relative movement of two elements with full motion capability in space need to provide six Degrees Of Freedom (DOF) at their moveable output member or end effector (usually with respect to the ground or base), which corresponds to the maximum spatiality of a rigid body in space. Three DOF are needed to perform translations in space and three DOF for rotations.
For most applications, only a subset of these six DOF is needed. So, the complexity and cost of the robotic structure can be reduced. Further, performance may be increased by choosing a design with fewer than six active (or powered) DOF, the motions along the remaining non-powered DOF being rigidly constrained (e.g. to ground or a fixed structure), or left free to move (or compliant) in some very special designs (e.g. path generation or compliant mechanisms).
In so-called redundant designs, there are more than six DOF (or mobility) in the mechanical structure, which can be useful to control the posture in space (or how the limbs occupy space). This allows, for example, to accommodate special space requirements or to avoid obstacles. As an example, a snake-like robot with a large amount of articulated segments (more than six) providing each one DOF can choose from different possible paths to reach a given target, even though it's head or end effector can only provide six DOF. Position and orientation of a single rigid body like the end effector is also called pose, whereas posture refers to all the limbs including the end effector. Some devices incorporate additional DOF for specific features, as for example a pincher, gripper, scissor, or even articulated finger-like structures to provide advanced grasping capabilities.
As common actuators (and sensors) provide motion along only a single DOF joint, either an active translational DOF (or prismatic joint) along an axis or an active rotational DOF (or pivot joint) around an axis, a kinematics structure (or an arrangement of links and active and passive joints or more generally speaking an arrangement of kinematics bonds) is required to obtain the desired multiple DOF motion of the end effector. Many different kinematics structures with up to six DOF are known. They can be divided in three main groups: serial, parallel and hybrid kinematics structures.
“Serial” kinematics structures (also called open-loop structures) are built of a single chain of rigid links interconnected by actuated joints. This serial arrangement of links and active joints offers large motion ranges, but inertia (or mass) is high (since actuators are carried by the structure) and stiffness and strength are low (since the complete forces and torques are transmitted through every link and joint of the kinematics chain, adding their compliances and weights). The resulting mechanical eigen-frequencies (related to the ratio between stiffness and inertia) and motion dynamics are low; undesired bending and vibrations lead to low precision.
“Parallel” kinematics have more than one kinematics chain connecting the base to the end effector, each chain having one actuated joint, the others being passive joints, thus enabling to reduce inertia and weight (since heavy parts of actuators are located close to or directly on the ground, which has also a positive influence in reducing complexity and wear of power and signal connections from the ground to these actuators) and to increase stiffness and strength (since multiple chains act “in parallel” on the end effector, each chain transmitting only part of the total forces and torques applied on the end effector). The resulting mechanical eigen-frequencies and motion dynamics are therefore higher than for serial kinematics structures. Drawbacks are reduced motion ranges (since the resulting workspace is defined by the intersection of several chains, which can furthermore interfere with each other and let undesired singular or unstable postures arise within the workspace), reduced accessibility to the end effector, greater volume occupied by moving mechanical parts and greater complexity due to the additional passive joints.
A third kind of kinematics structures called “hybrid” can offer a way in between pure serial and pure parallel structures to at least partially reduce some of their respective drawbacks. Hybrid structures can for example offer higher motion ranges than fully parallel designs, while being stiffer and having less inertia and weight than serial kinematics designs. Some of them have multiple chains arranged in parallel using more than one actuated joint per chain (or complex limbs), while others stack several parallel kinematics structures in series.
In many applications, the end effector of a robotic structure carries an object or a tool that has to be positioned and oriented in space. A general rotational movement requires the definition of a rotation center (RC) (or a rotation axis in case of a one DOF rotational motion), usually related to the carried object or tool and located at a given point of interest, as for example its center or tip. In order to avoid interference issues with moving mechanical parts and to allow for sufficient accessibility to the carried object or tool, the carried object or tool and its associated rotation center are generally located at a distance (remote) from the end effector fixture in the outer side of the volume occupied by these moving mechanical parts. The choice of the RC location with respect to the kinematics structure needs to take into account practical requirements of geometrical nature and will greatly influence the usable range of motion for a given kinematics structure. To be more precise, the dexterous workspace is the one being greatly influenced by the choice of the tool center point (TCP), which geometrically defines and is coincident with the RC on the end effector. The dexterous workspace is defined by the set of all positions that can be reached in translation by the end effector's TCP while ensuring a minimal given rotational motion range around the TCP.
Any given kinematics structure has inherent or natural TCP locations where its dexterous workspace is optimal. Choosing a remote TCP located at a distance (or offset) with respect to an inherently optimal TCP will define a remote RC (RRC) or remote center of motion (RCM), which will inevitably reduce the dexterous workspace in this remote TCP.
A rotational movement around such a RRC will generate translational movements of the end effector on a spherical surface (or circular path in case of a one DOF rotational motion) to compensate for the distance between inherent RC and RRC. These compensating translational movements are subtracted from the initially available translational motion range, the remaining usable translational motion range being thereby reduced. This dexterous workspace reduction is generally associated with an increase of the apparent inertia at the remote TCP and a reduction of the maximum rotational velocity.
In order to reduce or even to annihilate the amplitude of these compensating translational movements, kinematics structures should be spatially configured for a given application or specifically designed in such a way that their natural RC is inherently located close to or even at the exact desired remote TCP, thereby reducing only little or even none of the translational motion ranges and dexterous workspace. Known parallel and hybrid kinematics structures usually have their natural RC located somewhere in the inner side of the volume occupied by its moving mechanical parts with little or no accessibility to it, and have inherently low angular motion ranges due to mechanical interference issues and generally have undesired singular postures within the workspace. For these structures, choosing a remote TCP location on the outer side of the volume occupied by its moving mechanical parts substantially reduces further its initially limited dexterous workspace.
To partly overcome these limitations, some parallel and hybrid kinematics designs incorporate special one DOF pivot joints or joint arrangements with inherent RRC. For kinematics structures limited to motions including only one rotational DOF, such an existing RRC pivot joint is suitable and many different examples can be found.
If a two or three DOF RRC joint is needed, it is always possible to use a serial kinematics arrangement of two or three discrete one DOF pivot joints respectively, some or all of which can be of RRC type. However, this arrangement does not completely solve the interference and accessibility issues stated above, especially in designs where several kinematics chains are arranged in parallel.
In general, providing for relative movements between two members or elements, known devices based on parallel and hybrid kinematics structures inherently have low rotational motion ranges and dexterous workspace (due to mechanical interferences between relatively moving parts and to presence of undesired singular postures) and do not provide sufficient accessibility to their inherent optimal RRC.